Pathwise uniqueness of one-dimensional SDEs driven by one-sided stable processes

2013/05/23 by Hua Ren, Ren, Hua
Economics, Econometrics and Finance · #Economic theories and models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1305.5298

Abstract

For α∈ (0,1), we consider stochastic differential equations driven by one-sided stable processes of order α: dX_t= ϕ(X_t-) dZ_t. We prove that pathwise uniqueness holds for this equation under the assumptions that ϕ is continuous, non-decreasing and positive on \R. A counterexample is given to show that the positivity of ϕ is crucial for pathwise uniqueness to hold.

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